Understanding Systems of Inequalities

The video tutorial explains how to determine a system of inequalities from a graph. It covers analyzing a parabola and a red line, focusing on their equations, intercepts, and vertex. The tutorial emphasizes the importance of using test points to select the correct inequality when the equation is not solved for y. It provides a step-by-step approach to understanding the graph's shaded region and the inequalities that define it.

What type of inequality symbols are used when both graphs are solid?

• Not equal to

• Less than or greater than

• Less than or equal to or greater than or equal to

• Equal to

What is the vertex form of a quadratic function?

• y = a(x + h)^2 + k

• y = a(x - h)^2 + k

• y = a(x - h)^2 - k

• y = a(x + h)^2 - k

If a parabola opens downward, what can be said about the value of 'a' in its vertex form?

• a is positive

• a is zero

• a is undefined

• a is negative

What is the slope of the red line discussed in the video?

• 1

• 1/2

• 2

• 0

What is the vertical intercept of the red line?

• (-3, 0)

• (0, 3)

• (0, -3)

• (3, 0)

Which equation represents the red line based on its intercepts?

• x + 2y = 6

• 2x + y = 6

• 2x - y = 6

• x - 2y = 6

Why is it important to select a test point when the inequality is not solved for y?

• To decide whether to shade above or below the line

• To calculate the vertex

• To find the intercepts

• To determine the slope

What test point is used to determine the correct inequality for the red line?

• (0, 0)

• (6, 0)

• (2, 0)

• (0, -3)

What is the result when substituting the test point (2, 0) into the inequality x - 2y ≤ 6?

• 2 ≥ 6, which is false

• 0 ≥ 6, which is false

• 2 ≤ 6, which is true

• 0 ≤ 6, which is true

What should be done if the inequality is not solved for y?

• Use the slope to determine shading

• Select a test point to determine shading

• Use the vertex to determine shading

• Use the intercepts to determine shading